Impact of rotation on a cold atom interferometer and compensation strategy

TL;DR

The paper addresses rotation-induced degradation of ultra-precise atom interferometers by developing a comprehensive analytical model that quantifies how Coriolis, Euler, and centrifugal accelerations affect phase and contrast. It validates the model experimentally using a hybrid atomic-electrostatic accelerometer in which the electrostatic proof-mass serves as the interferometer mirror, and demonstrates a rotation-compensation approach that counter-rotates the mirror to stabilize $|\vec{k}_{\mathrm{eff}}|$, recovering interferometer contrast to above 90%. The results show strong agreement for contrast loss and substantial, though incomplete, cancellation of rotation-induced phase shifts, highlighting residual Euler and centrifugal terms that constrain performance in dynamic space environments. The findings support the feasibility of high-performance onboard cold-atom inertial sensors for space gravimetry, while outlining avenues for reducing phase biases and further improving compensation strategies in orbit.

Abstract

Rotations play a detrimental role in achieving ultra-high-performance inertial measurements with an atom interferometer, leading potentially to a total loss of interference contrast and the emergence of dominant phase shift biases. This becomes particularly significant when considering operation in dynamic conditions such as those encountered in Earth orbiting satellites in the perspective of future space gravity missions on-boarding a cold atom accelerometer. We study in this context the impact of rotation on the phase shift and contrast of an atom interferometer and investigate mitigation strategies. An analytical model is derived and compared to experimental demonstrations carried out using an original setup in which the well-controlled proof-mass of a space electrostatic accelerometer is used as the retro-reflection mirror of a cold atom gravimeter. By properly counter-rotating the electrostatic proof-mass, we demonstrate for instance the possibility of recovering the interferometer contrast, otherwise equal to zero, to a level better than 90%, in both cases of constant angular velocities or in presence of angular accelerations. Our results demonstrate the possibility to perform high performance inertial measurements with a cold atom interferometer in a challenging environments.

Figures (17)

• Figure 1: Space-time diagram of a Mach-Zehnder atomic accelerometer measuring along the X axis. The three long red rectangles are the laser pulses $\frac{\pi}{2}-\pi-\frac{\pi}{2}$ driving the atomic transitions between the ground state $\ket{g,\vec{p}}$ and the excited state $\ket{e,\vec{p}+\hbar \vec{k}_{\mathrm{eff}}}$. The atoms free fall for a time $t_0$ before the start of the interferometer. The first and third laser pulses put the atoms in a superposition of states and have a duration $\tau$. The second pulse redirects the atom cloud and lasts $2\tau$. The free evolution of the atoms between the pulses lasts $T\gg \tau$. Experimentally, $t_0=10ms$, $T=46ms$ and $\tau=4µ s$.
• Figure 2: Description of the rotating frames: the sensor frame $\mathcal{R}_{S}$ and the mirror frame $\mathcal{R}_{M}$ in rotation in the laboratory frame $\mathcal{R}_{L}$. The blue rectangle is the table supporting the sensor. This table and the incoming laser are fixed in $\mathcal{R}_{S}$ and rotate around $O$ the center of rotation of the sensor. The yellow rectangle is the retro-reflection mirror rotating around M. $\vec{x}_r$ is the unitary vector in the direction of the reflected laser in the mirror and A the center of the atom cloud.
• Figure 3: Experimental setup composed of a cold atom gravimeter, an electrostatic accelerometer, a two axis gyroscope, a passive isolation platform and piezo-electric actuators (PZT B and PZT C) allowing the whole setup to be rotated.
• Figure 4: Electrostatic accelerometer proof-mass and electrodes. The arrangement of the electrodes allows the control of the six degrees of freedom of the proof-mass.
• Figure 5: Atomic interference fringes collected by scanning the two-photon Raman laser frequency rate $\alpha$. The horizontal axis is the pseudo acceleration induced by the scan of $\alpha$. The blue, respectively green, circles are the measured proportion of atoms in the excited state at the output of the interferometer in the absence, respectively in the presence, of a mirror rotation. Solid blue, respectively green, line is the sinusoidal fit of the experimental data in the absence, respectively in the presence, of a mirror rotation with a mean angular acceleration is $\dot{\Omega}^0_M=-52.4rad \per \square s$ and a mean angular velocity close to zero.